A search for the parity-nonconserving contribution to the $\gamma$ decay of ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$ has been made. A complete description of the experimental technique is presented. The angular distribution of the 363-keV line of ${}_{}{}^{159}{}_{}{}^{}\mathrm{Tb}$ was measured with a pair of Ge(Li) detectors. The ${}_{}{}^{159}{}_{}{}^{}\mathrm{Gd}$ parent atoms were located in the +453-kG hyperfine field of Gd${\mathrm{Fe}}_2$ held at 28 mK by a ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ dilution refrigerator. The resulting 7% polarization of the ${}_{}{}^{159}{}_{}{}^{}\mathrm{Gd}$ led to a $P_1\left(cos\Theta \right)$ term of +(2.7 ± 1.8) × ${10}^{-4\mathrm{}}$ in the $\gamma$-ray angular distribution, where $\Theta$ is measured with respect to the nuclear polarization. Thus, for full Tb polarization, the asymmetry would be +(4.5 ± 3.0) × ${10}^{-3\mathrm{}}$ $P_1\left(cos\Theta \right)$, peaked in the direction of Tb nuclear spin alignment. This sign of the $P_1\left(cos\Theta \right)$ term is based on an assumed negative moment of the ${}_{}{}^{159}{}_{}{}^{}\mathrm{Gd}$ parent. We measure the magnitude of this moment to be $(0.22\mathrm{}\pm 0.05){\mu }_N$.

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